The underlying data consist of just four numbers: the wage gaps between race and gender in the U.S., considered simply from an aggregate median personal income perspective. The analyst adopts the median annual salary of a white male worker as a baseline. Then, s/he imputes the number of extra days that others must work to attain the same level of income. For example, the median Asian female worker must work 64 extra days (at her daily salary level) to match the white guy's annual pay. Meanwhile, Hispanic female workers must work 324 days extra.

There are a host of reasons why the calendar metaphor backfired.

Firstly, it draws attention to an uncomfortable detail of the analysis - which papers over the fact that weekends or public holidays are counted as workdays. The coloring of the boxes compounds this issue. (And the designer also got confused and slipped up when applying the purple color for Hispanic women.)

Secondly, the calendar focuses on Year 2 while Year 1 lurks in the background - white men have to work to get that income (roughly $46,000 in 2017 according to the Census Bureau).

Thirdly, the calendar view exposes another sore point around the underlying analysis. In reality, the white male workers are continuing to earn wages during Year 2.

The realism of the calendar clashes with the hypothetical nature of the analysis.

***

One can just use a bar chart, comparing the number of extra days needed. The calendar design can be considered a set of overlapping bars, wrapped around the shape of a calendar.

The staid bars do not bring to life the extra toil - the message is that these women have to work harder to get the same amount of pay. This led me to a different metaphor - the white men got to the destination in a straight line but the women must go around loops (extra days) before reaching the same endpoint.

While the above is a rough sketch, I made sure that the total length of the lines including the loops roughly matches the total number of days the women needed to work to earn $46,000.

***

The above discussion focuses solely on the V(isual) corner of the Trifecta Checkup, but this data visualization is also interesting from the D(ata) perspective. Statisticians won't like such a simple analysis that ignores, among other things, the different mix of jobs and industries underlying these aggregate pay figures.

Now go to my other post on the sister (book) blog for a discussion of the underlying analysis.

This Financial Times chart paints the picture of the emerging trend in Wimbledon men’s tennis: the average age of players has been rising, and hits 30 years old for the first time ever in 2019.

The chart works brilliantly. Let's look at the design decisions that contributed to its success.

The chart contains a good amount of data and the presentation is carefully layered, with the layers nicely tied to some visual cues.

Readers are drawn immediately to the average line, which conveys the key statistical finding. The blue dot reinforces the key message, aided by the dotted line drawn at 30 years old. The single data label that shows a number also highlights the message.

Next, readers may notice the large font that is applied to selected players. This device draws attention to the human stories behind the dry data. Knowledgable fans may recall fondly when Borg, Becker and Chang burst onto the scene as teenagers.

Then, readers may pick up on the ticker-tape data that display the spread of ages of Wimbledon players in any given year. There is some shading involved, not clearly explained, but we surmise that it illustrates the range of ages of most of the contestants. In a sense, the range of probable ages and the average age tell the same story. The current trend of rising ages began around 2005.

Finally, a key data processing decision is disclosed in chart header and sub-header. The chart only plots the players who reached the fourth round (16). Like most decisions involved in data analysis, this choice has both desirable and undesirable effects. I like it because it thins out the data. The chart would have appeared more cluttered otherwise, in a negative way.

The removal of players eliminated in the early rounds limits the conclusion that one can draw from the chart. We are tempted to generalize the finding, saying that the average men’s player has increased in age – that was what I said in the first paragraph. Thinking about that for a second, I am not so sure the general statement is valid.

The overall field might have gone younger or not grown older, even as the older players assert their presence in the tournament. (This article provides side evidence that the conjecture might be true: the author looked at the average age of players in the top 100 ATP ranking versus top 1000, and learned that the average age of the top 1000 has barely shifted while the top 100 players have definitely grown older.)

So kudos to these reporters for writing a careful headline that stays true to the analysis.

This chart about Wimbledon players hits the Trifecta. It has an interesting – to some, surprising – message (Q). It demonstrates thoughtful processing and analysis of the data (D). And the visual design fits well with its intended message (V). (For a comprehensive guide to the Trifecta Checkup, see here.)

In the recent issue of Madolyn Smith’s Conversations with Data newsletter hosted by DataJournalism.com, she discusses “bad charts,” featuring submissions from several dataviz bloggers, including myself.

What is a “bad chart”? Based on this collection of curated "bad charts", it is not easy to nail down “bad-ness”. The common theme is the mismatch between the message intended by the designer and the message received by the reader, a classic error of communication. How such mismatch arises depends on the specific example. I am able to divide the “bad charts” into two groups: charts that are misinterpreted, and charts that are misleading.

Charts that are misinterpreted

The Causes of Death entry, submitted by Alberto Cairo, is a “well-designed” chart that requires “reading the story where it is inserted and the numerous caveats.” So readers may misinterpret the chart if they do not also partake the story at Our World in Data which runs over 1,500 words not including the appendix.

The map of Canada, submitted by Highsoft, highlights in green the provinces where the majority of residents are members of the First Nations. The “bad” is that readers may incorrectly “infer that a sizable part of the Canadian population is First Nations.”

In these two examples, the graphic is considered adequate and yet the reader fails to glean the message intended by the designer.

Charts that are misleading

Two fellow bloggers, Cole Knaflic and Jon Schwabish, offer the advice to start bars at zero (here's my take on this rule). The “bad” is the distortion introduced when encoding the data into the visual elements.

The Color-blindness pictogram, submitted by Severino Ribecca, commits a similar faux pas. To compare the rates among men and women, the pictograms should use the same baseline.

In these examples, readers who correctly read the charts nonetheless leave with the wrong message. (We assume the designer does not intend to distort the data.) The readers misinterpret the data without misinterpreting the graphics.

Using the Trifecta Checkup

In the Trifecta Checkup framework, these problems are second-level problems, represented by the green arrows linking up the three corners. (Click here to learn more about using the Trifecta Checkup.)

The visual design of the Causes of Death chart is not under question, and the intended message of the author is clearly articulated in the text. Our concern is that the reader must go outside the graphic to learn the full message. This suggests a problem related to the syncing between the visual design and the message (the QV edge).

By contrast, in the Color Blindness graphic, the data are not under question, nor is the use of pictograms. Our concern is how the data got turned into figurines. This suggests a problem related to the syncing between the data and the visual (the DV edge).

***

When you complain about a misleading chart, or a chart being misinterpreted, what do you really mean? Is it a visual design problem? a data problem? Or is it a syncing problem between two components?

The editors of ASA's Amstat News certainly got my attention, in a recent article on school counselling. A research team asked two questions. The first was HOW ARE YOU FELINE?

Stats and cats. The pun got my attention and presumably also made others stop and wonder. The second question was HOW DO YOU REMEMBER FEELING while you were taking a college statistics course? Well, it's hard to imagine the average response to that question would be positive.

These paragraphs convey two crucial pieces of information: the structure of the analysis, and its insights.

The two survey questions measure two states of experiences, described as current versus recalled. Then the individual affects (of which there were 16 plus an option of "other") are scored on two dimensions, pleasure and arousal. Each affect maps to high or low pleasure, and separately to high or low arousal.

The research insight is that current experience was noticably higher than recalled experience on the pleasure dimension but both experiences were similar on the arousal dimension.

Any visualization of this research must bring out this insight.

***

Here is an attempt to illustrate those paragraphs:

The primary conclusion can be read from the four simple pie charts in the middle of the page. The color scheme shines light on which affects are coded as high or low for each dimension. For example, "distressed" is scored as showing low pleasure and high arousal.

A successful data visualization for this situation has to bring out the conclusion drawn at the aggregated level, while explaining the connection between individual affects and their aggregates.

From a Trifecta Checkup perspective, the chart has a clear question: are consumers getting what they wanted to read in the news they are reading?

Nevertheless, the chart is a visual mess, and the underlying data analytics fail to convince. So, it’s a Type DV chart. (See this overview of the Trifecta Checkup for the taxonomy.)

***

The designer did something tricky with the axis but the trick went off the rails. The underlying data consist of two set of ranks, one for news people consumed and the other for news people wanted covered. With 14 topics included in the study, the two data series contain the same values, 1 to 14. The trick is to collapse both axes onto one. The trouble is that the same value occurs twice, and the reader must differentiate the plot symbols (triangle or circle) to figure out which is which.

It does not help that the lines look like arrows suggesting movement. Without first reading the text, readers may assume that topics change in rank between two periods of time. Some topics moved right, increasing in importance while others shifted left.

The design wisely separated the 14 topics into three logical groups. The blue group comprises news topics for which “want covered” ranking exceeds the “read” ranking. The orange group has the opposite disposition such that the data for “read” sit to the right side of the data for “want covered”. Unfortunately, the legend up top does more harm than good: it literally takes sides!

The two sets of ranks are basically uncorrelated, as the regression line is almost flat, with “R-squared” of 0.02.

The analyst tried to "rescue" the data in the following way. Draw the 45-degree line, and color the points above the diagonal blue, and those below the diagonal orange. Color the points on the line gray. Then, write stories about those three subgroups.

Further, the ranking of what was read came from Parse.ly, which appears to be surveillance data (“traffic analytics”) while the ranking of what people want covered came from an Axios/SurveyMonkey poll. As for as I could tell, there was no attempt to establish that the two populations are compatible and comparable.

Earlier this month, the bombs in Sri Lanka led to some data graphics in the media, educating us on the religious tensions within the island nation. I like this effort by Reuters using small multiples to show which religions are represented in which districts of Sri Lanka (lifted from their twitter feed):

The key to reading this map is the top legend. From there, you'll notice that many of the color blocks, especially for Muslims and Catholics are well short of 50 percent. The absence of the darkest tints of green and blue conveys important information. Looking at the blue map by itself misleads - Catholics are in the minority in every district except one. In this setup, readers are expected to compare between maps, and between map and legend.

The overall distribution at the bottom of the chart is a nice piece of context.

***

The above design isolates each religion in its own chart, and displays the spatial spheres of influence. I played around with using different ways of paneling the small multiples.

In the following graphic, the panels represent the level of dominance within each district. The first panel shows the districts in which the top religion is practiced by at least 70 percent of the population (if religions were evenly distributed across all districts, we expect 70 percent of each to be Buddhists.) The second panel shows the religions that account for 40 to 70 percent of the district's residents. By this definition, no district can appear on both the left and middle maps. This division is effective at showing districts with one dominant religion, and those that are "mixed".

In the middle panel, the displayed religion represents the top religion in a mixed district. The last panel shows the second religion in each mixed district, and these religions typically take up between 25 and 40 percent of the residents.

The chart shows that other than Buddhists, Hinduism is the only religion that dominates specific districts, concentrated at the northern end of the island. The districts along the east and west coasts and the "neck" are mixed with the top religion accounting for 40 to 70 percent of the residents. By assimilating the second and the third panels, the reader sees the top and the second religions in each of these mixed districts.

***

This example shows why in the Trifecta Checkup, the Visual is a separate corner from the Question and the Data. Both maps utilize the same visual design, in terms of forms and colors and so on, but they deliver different expereinces to readers by answering different questions, and cutting the data differently.

It's a great example of highly effective data visualization. The names on the board are sake brands.

The menu (a version of a data table) is the conventional way of displaying this information.

The Question

Customers are selecting a sake. They don't have a favorite, or don't recognize many of these brands. They know a bit about their preferences: I like full-bodied, or I want the dry one.

The Data

On a menu, the key data are missing. So the first order of business is to find data on full- and light-bodied, and dry and sweet. The pricing data are omitted, possibly because it clutters up the design, or because the shop doesn't want customers to focus on price - or both.

The Visual

The design uses a scatter plot. The customer finds the right quartet, thus narrowing the choices to three or four brands. Then, the positions on the two axes allow the customer to drill down further.

This user experience is leaps and bounds above scanning a list of names, and asking someone who may or may not be an expert.

Back to the Data

The success of the design depends crucially on selecting the right data. Baked into the scatter plot is the assumption that the designer knows the two factors most influential to the customer's decision. Technically, this is a "variable selection" problem: of all factors determining the brand choice, which two are the most important?

Think about the downside of selecting the wrong factors. Then, the scatter plot makes it harder to choose the sake compared to the menu.

Reader Aleksander B. sent me to the following chart in the Daily Mail, with the note that "the usage of area/bubble chart in combination with bar alignment is not very useful." (link)

One can't argue with that statement. This chart fails the self-sufficiency test: anyone reading the chart is reading the data printed on the right column, and does not gain anything from the visual elements (thus, the visual representation is not self-sufficient). As a quick check, the size of the risk for "motorcycle" should be about 30 times larger than that of "car"; the size of the risk for "car" should be 100 times larger than that of "airplane". The risk of riding motorcycles then is roughly 3,000 times that of flying in an airplane.

As a bar chart, both the widths and the heights of the bars vary; and the last row presents a further challenge as the bubble for the airplane does not touch the baseline.

***

Besides the Visual, the Data issues are also quite hard. This is how Aleksander describes it: "as a reader I don't want to calculate all my travel distances and then do more math to compare different ways of traveling."

The reader wants to make smarter decisions about travel based on the data provided here. Aleksandr proposes one such problem:

In terms of probability it is also easier to understand: "I am sitting in my car in strong traffic. At the end in 1 hour I will make only 10 miles so what's the probability that I will die? Is it higher or lower than 1 hour in Amtrak train?"

The underlying choice is between driving and taking Amtrak for a particular trip. This comparison is relevant because those two modes of transport are substitutes for this trip.

One Data issue with the chart is that riding a motorcycle and flying in a plane are rarely substitutes.

***

A way out is to do the math on behalf of your reader. The metric of deaths per 1 billion passenger-miles is not intuitive for a casual reader. A more relevant question is what's the chance of dying from the time I spend per year of driving (or riding a plane). Because the chance will be very tiny, it is easier to express the risk as the number of years of travel before I expect to see one death.

Let's assume someone drives 300 days per year, and 100 miles per day so that each year, this driver contributes 30,000 passenger-miles to the U.S. total (which is 3.2 trillion). We convert 7.3 deaths per 1 billion passenger-miles to 1 death per 137 million passenger-miles. Since this driver does 30K per year, it will take (137 million / 30K) = about 4,500 years to see one death on average. This calculation assumes that the driver drives alone. It's straightforward to adjust the estimate if the average occupancy is higher than 1.

Now, let's consider someone who flies once a month (one outbound trip plus one return trip). We assume that each plane takes on average 100 passengers (including our protagonist), and each trip covers on average 1,000 miles. Then each of these flights contributes 100,000 passenger-miles. In a year, the 24 trips contribute 2.4 million passenger-miles. The risk of flying is listed at 0.07 deaths per 1 billion, which we convert to 1 death per 14 billion passenger-miles. On this flight schedule, it will take (14 billion / 2.4 million) = almost 6,000 years to see one death on average.

For the average person on those travel schedules, there is nothing to worry about.

***

Comparing driving and flying is only valid for those trips in which you have a choice. So a proper comparison requires breaking down the average risks into components (e.g. focusing on shorter trips).

The above calculation also suggests that the risk is not evenly spread out throughout the population, despite the use of an overall average. A trucker who is on the road every work day is clearly subject to higher risk than an occasional driver who makes a few trips on rental cars each year.

There is a further important point to note about flight risk, due to MIT professor Arnold Barnett. He has long criticized the use of deaths per billion passenger-miles as a risk metric for flights. (In Chapter 5 of Numbers Rule Your World (link), I explain some of Arnie's research on flight risk.) The problem is that almost all fatal crashes involving planes happen soon after take-off or not long before landing.

Through Twitter, Danny H. submitted the following chart that shows a tiny 0.3 percent of Youtube creators generate almost 40 percent of all viewing on the platform. He asks for ideas about how to present lop-sided data that follow the "80/20" rule.

In the classic 80/20 rule, 20 percent of the units account for 80 percent of the data. The percentages vary, so long as the first number is small relative to the second. In the Youtube example, 0.3 percent is compared to 40 percent. The underlying reason for such lop-sidedness is the differential importance of the units. The top units are much more important than the bottom units, as measured by their contribution to the data.

I sense a bit of "loss aversion" on this chart (explained here). The designer color-coded the views data into blue, brown and gray but didn't have it in him/her to throw out the sub-categories, which slows down cognition and adds hardly to our understanding.

I like the chart title that explains what it is about.

Turning to the D corner of the Trifecta Checkup for a moment, I suspect that this chart only counts videos that have at least one play. (Zero-play videos do not show up in a play log.) For a site like Youtube, a large proportion of uploaded videos have no views and thus, many creators also have no views.

***

My initial reaction on Twitter is to use a mirrored bar chart, like this:

I ended up spending quite a bit of time exploring other concepts. In particular, I like to find an integrated way to present this information. Most charts, such as the mirrored bar chart, a Bumps chart (slopegraph), and Lorenz chart, keep the two series of percentages separate.

Also, the biggest bar (the gray bar showing 97% of all creators) highlights the least important Youtubers while the top creators ("super-creators") are cramped inside a slither of a bar, which is invisible in the original chart.

What I came up with is a bar-density plot, where I use density to encode the importance of creators, and bar lengths to encode the distribution of views.

Each bar is divided into pieces, with the number of pieces proportional to the number of creators in each segment. This has the happy result that the super-creators are represented by large (red) pieces while the least important creators by little (gray) pieces.

The embedded tessellation shows the structure of the data: the bottom third of the views are generated by a huge number of creators, producing a few views each - resulting in a high density. The top 38% of the views correspond to a small number of super-creators - appropriately shown by a bar of low density.

For those interested in technicalities, I embed a Voronoi diagram inside each bar, with randomly placed points. (There will be a companion post later this week with some more details, and R code.)

Here is what the bar-density plot looks like when the distribution is essentially uniform:

The density inside each bar is roughly the same, indicating that the creators are roughly equally important.

P.S.

1) The next post on the bar-density plot, with some experimental R code, will be available here.

Now, look at the bubble chart at the bottom. Here it is - with all the data except the first number removed:

It is impossible to know how fast the four other train systems run after I removed the numbers. The only way a reader can comprehend this chart is to read the data inside the bubbles. This chart fails the "self-sufficiency test". The self-sufficiency test asks how much work the visual elements on the chart are doing to communicate the data; in this case, the bubbles do nothing at all.

Another problem: this chart buries its lede. The message is in the caption: how California's bullet train rates against other fast train systems. California's train speed of 220 mph is only mentioned in the text but not found in the visual.

Here is a chart that draws attention to the key message:

In a Trifecta checkup, we improved this chart by bringing the visual in sync with the central question of the chart.